Oh well I guess snark can be justified as necessary to keeping standards above some rock bottom. Anyway, I did wonder whether this article on the Renaissance and innovation was the silliest thing written on either. Even ignoring the fact that he is about half a millennium out in equating the mediaeval period with the ‘dark ages’ there’s a deeper deliciousness to the way in which he imagines that, by describing a period he has explained it. “It wasn’t just a change of culture that made Western Europe so conducive to innovation at that time. It was also a change of mindset”. Innovation thrived in the Renaissance because of its more innovative culture – not only that but it’s more innovative mindset. The sedative worked because of its dormative qualities.

Anyway, for your delectation it is reproduced below:

In my new book, “The Four Lenses of Innovation,” I examine that marvelous period of European history between the fourteenth and the seventeenth centuries that we call the Renaissance. And I ask what exactly led to such an explosion of creativity and invention back then, following what was essentially a thousand years of stagnation during the Middle Ages. And I believe there’s a two-fold answer.

The first factor was this new cultural environment that came about due to the rapid urbanization of Northern Italy, and in particular the emergence of powerful city-states like Florence, Venice, and Milan.

That’s where rich banking families began to compete with each other to fund the work of the greatest painters, sculptors, architects, writers, philosophers, and scientists of their day. This brought together a variety of highly talented people from the worlds of art, education, and science, who then had the opportunity to cross-pollinate ideas and insights from their different fields, disciplines, and cultures. So it was an amazing intersection point that became a fertile breeding ground for innovation – rather like the Internet is today.

But I also believe there was more to the equation. It wasn’t just a change of culture that made Western Europe so conducive to innovation at that time. It was also a change of mindset. We have to remember that during the medieval period – or the so-called “Dark Ages” – there was a huge constraint on new thinking and progress. This essentially came from the medieval church, which enforced very strong orthodoxies about the way the world was supposed to work and how people were supposed to think. And if you tried to challenge those notions, you were likely to be burned at the stake as a heretic. But along with the Renaissance came a new philosophy called humanism, which to a great extent liberated the human mind from the constraints of medieval superstition, and encouraged people to tap into their own intellectual and creative capacities in unprecedented ways. So suddenly there was a whole new way of thinking – a new way of looking at the world – that introduced fresh perspectives. And guess what? Those perspectives are exactly the ones I described earlier – Challenging Orthodoxies, Harnessing Trends, Leveraging Resources in new ways, and Understanding Needs. They were just as much the drivers of Renaissance creativity and invention as the culture that allowed them to flourish. And that’s why I decided to focus my new book on these four lenses of innovation.

So if we are going to create a culture of innovation today inside our organizations, we are going to have to understand not just the environments that enhance our capacity to dream up and introduce new things, but also the thinking processes inside the human mind that lead innovators to their “Eureka moments.” Senior executives should be asking themselves, “Does our company already have a Renaissance-type corporate culture that functions as a powerful catalyst for continuous innovation? Or does it have more of a medieval management culture that is acting as an innovation anchor by holding people back in their efforts to be creative?”

Yes, it’s almost inconceivable, isn’t it, that until the Arabs brought the Indian zero, we just had no conception whatsoever that there could be none of something … or indeed that all nothings are equivalent.

Or do you perhaps think that what the Arabs really brought us was a power-of-10 positional number system in which a zero was an essential but minor component.

After all, when you do your arithmetic by abacus or its equivalent, and written numbers are just the recorded result of calculations, then you really don’t need a zero, do you.

Interesting question!
Some Western mystics definitely had conceptions of the infinite and of complete ‘present-absence’, but were there symbols of zero as explicit as ‘0’ prior to then, I do not know?
Re “do your arithmetic”
Obviously power-of-10 was terribly important the the development of finance and banking, which does need maths,no? –

Precisely. And a positional power-of-n (ten fingers = our number system base, only much later power-of-2 (binary), power-of-8 (octal) and power-of-12 (duodecimal), or power-of-13 if you want to know when multiplying 6 by 9 gives 42) needs a zero digit available for some positions simply to get the number right.

But just because the Romans, Greeks and Chinese used abacus calculations rather than the number system based arithmetic operations that is till (sometimes) taught in schools today doesn’t mean they had no concept of zero. Of course they were aware of ‘an absence’, they just didn’t need a specific digit to represent it.

The scientific revolution would also been next to impossible without ‘0’, and that revolution, which began in the latter part of the Renaissance really was the engine room of the ‘ rise of the west’, no?

Oh, I don’t think the so-called ‘scientific revolution’ owed anything to the use of a specific symbol to represent zero. Admittedly, some of the later numerical calculations would have been somewhat messy to represent eg Avogadro’s number, 6.023 * 10^23, wouldn’t be exactly easy to express in Roman numerals.

Nonetheless, Roman numerals, not be a power-of-n positional number system does not need a specific symbol for zero, but can adequately represent a very wide range of numbers.

Anyhow, Al Haytham wrote what was probably the first model scientific paper with all the relevant sections (description of experiment, methodology and procedures, results and outcomes, analysis and conclusions) that are considered essential to modern publishable scientific papers.

So no, I don’t think the ‘scientific revolution’ (at least the one that began long before the Renaissance) owes anything to he use of one specific digit to represent zero. It might have owed a fair bit to the einvention of logarithms and the slide rule though :-)

yes well this isn’t the first time you’ve quoted that reference, but nobody responded the last time, so let me do the courteous thing and inquire: just what point are you trying to make ?

Is it that Steve Shapin lays stress on the mathematicisation of science in the 17th century ? is he really trying to say that it wasn’t so much a “scientific” revolution as a mathematical one ?

Mathematics experienced something of an explosive growth in the Renaissance and later and it became very much the preferred mode for expressing many branches of science (though mainly physics and astronomy).

But I would remind you that even though the Greeks had a confused view of the zero symbol (“how can a nothing be something ?”) they nonetheless did a lot of original maths in geometry (Euclid and Pythagoras) and number theory despite their numerical system being about as unwieldy as the Roman.

They also had some theory work on the sum of a near-infinite number of very small things, so they formulated the original conception of the calculus (at least of integration, anyway).

They may not have ‘discovered’ Riemann space or Hilbert space, but then, neither did anybody else.

I think that the significance of zero (and maths) was that it allowed a rapid development of representation of all kinds of complex relationships in a ‘universal’ way .
And the Renaissance was (to some degree ) a rebirth, no?

I think a mystery about the Renaissance is how was it that a whole number of mostly preexisting and often apparently unrelated components (some of which were not European) all in a relatively sudden way came together – created something unmistakably new and different .

GrueBleen
To give an example of things coming together in surprising new ways, Giotto and Fibonacci both died well before 1400 (unseal date for the end of the middle ages). How it was that Piero Della Francesca was (only a 100 or so years later) able to so well integrate those two new and apparently unrelated ways of representation, is a mystery.

Ah well, I’ll give up trying to persuade you that the use of a specific symbol for zero isn’t all that important, even though it isn’t. Most maths really doesn’t make use of a power-of-n positional number system.

Ok then, your point is the power of open-minded eclecticism – the ability to recognise and use an idea/concept/method/whatever regardless of where it came from.

And the opposite of the self-absorbed belief in ‘exceptionalism’ that afflicted the Chinese for most of their history, and which came to help destroy the British Empire and is now afflicting the USA in increasing intensity.

One only has to look at the Roman Empire – the first truly eclectic empire (look at how much the Romans learned from the Carthaginians, for instance). Almost all ‘great’ states/empires start out at least a little eclectic, and almost all end up in an ‘exceptionalism’ paralysis. So it goes.

Indeed, the only empire I can think of that fell (almost totally) but came again (sort of) is the Roman (unless you don’t think Italians are Romans who speak Modern Latin).

I defer to your knowledge re ‘0’ : it is ,I think the case that the original Fibonacci number set did not start with zero, yes ?

BTW
Interesting thing is that ,after the Renaissance , Peiro basically became a footnote in the official art history books. His work was only rediscovered , between about 1920 and 1950, by the likes of Huxley ,George Orwell and others of that time and circle(s) . Phillip Guston put this sudden rebirth of interest in Piero’s work down to the fact that Piero saw the world, and painted it, ‘like he was a [ intelligent skilled] ” alien”‘, seeing for first time .

The zero digit was important, not really in its own right but as a necessary component of the so-called Hindu-Arabic number system (that I have been referring to as the power-of-10 positional number system) which apparently was introduced to Europe by Leonardo Pisano (aka Fibonacci) in approximately 1200 (I didn’t know that until I looked it up – somehow I thought it was a little earlier than that – after all, Algebra had already been introduced before then). Though, as I mentioned, the zero symbol (digit) did cause the Greeks some philosophical problems.

But the ‘golden ratio’ was known to Euclid and Pythagoras, I understand, long before positional number systems. But Piero della Francesco was a ‘schooled’ mathematician and was well acquainted with Fibonacci’s work (amongst others). And being an accomplished artist – indeed a much undervalued one in your view – he must have been familiar with other Italian artists and their work.

As to Fibonacci’s series, I did a bit of a lookup and it seems that the sequence 0 1 1 2 … is the preferred way. Nonetheless, I seem to recall that when I encountered it, the zero wasn’t used and the series began 1 1 2 3 … But it was over 50 years ago that I first met Fibonacci, so I can’t swear to the validity of my memory – but whether or not the zero is included, the limit of successive terms as asymptotically approaching the golden ratio remains.

The Renaissance was an exciting time though, and it’s not surprising that all sorts of insights emerged sometimes cross-connecting different fields. it’s a lot harder now though – the low hanging fruit has almost all been picked.

Thanks.
I gather that the Fibonacci set (and possibly the famous use of the golden mean to graph the Fibonacci Spiral ?) were solutions to calculating the outcome of ,breading like rabbits , and therefore it originally began with 1+1 .

A few years ago I was able to spend several quiet days with Pieros “resurrection”, in the town of Sansepolcro. It really is the most amazing picture, you do not have to be a believer to know that you are looking at something that is ‘impossible ‘ yet quietly, totally convincing .
BTW There is a good essay on Piero by John Berger (a lower case marxist). Essays title is: The calculations of Piero ( written in the late 50s,) it is still available in various compilations of Berger’s writings, if you are near to a library they should have it(or be able to get it in on loan).